The calculus had its origin in the logical difficulties encountered by the ancient Greek mathematicians in their attempt to express their intuitive ideas in the ration or proportionalities of line, which vaguely recognized as continuous, in terms of numbers, which they regarded as discrete.
Indian mathematicians produced a number of works with some ideas of calculus. The formula for sum of the curve was first written by Aryabhata in 500 AD, order to find the volume of a cube, which was an important step in the development of integral calculus.
Methods for finding tangents were pioneered by Pierre Fermant (1601-1665), Isaac Barrow (1630-1677) and others. Barrow – who taught at Cambridge and was a major influence on Newton – was the first to understand the inverse relationship between differentiation and integration.
The analysis of problems, together with the free use of the suggestive infinitesimal and the more extensive application on numerical concept, led within a short time to the algorithms of Newton and Leibniz, which constitute the calculus.
Isaac Newton (1642-1727) developed calculus independently of Leibniz and applied it to the dynamics of bodied in Principia Mathematica, possibly the most important scientific treatise ever written.
He used variational principles to determine the shape of a body moving in air that encounters the least resistance.
Gottfried Wilhelm Leibniz was the other inventor of calculus. During his time, he and Newton argued over ten ownerships of their discoveries, each staking a claim as the inventor of calculus. This dogfight eventually involved many prominent mathematicians all over Europe. The dispute later known as the “Great Sulk”
Although both were instrumental in its creation, they thought of the fundamental concept in very different ways. While Newton considered variables changing with time, Leibniz thought of variables x and y as ranging over sequences of infinitely close values. For Newton the calculus was geometrical while Leibniz took it towards analysis.
Together with linear algebra including vector and matrix calculus introduced in the 1950s, calculus toady forms the core of mathematics education at the university levels, and simplified forms thereof fill the mathematics curricula in secondary schools.
History of calculus
